I agree that it's not a cost issue, probably would only take a couple of gallons. However, consider this: an automobile radiator is a closed system. If it is working properly, you are not adding water routinely, as you would in a coffee pot, home heating boiler, or an industrial boiler. In those applications, you are evaporating water, not recirculating it. Even in those applications, you can evaporate a huge volume of water before it produces significant scaling or sediment in the mud drum, in the case of marine and industrial boilers. One of my neighbors builds steam locomotives (about 3 feet long) as a hobby. These are total loss designs, which means that none of the condensate is recycled, thus all steam is the result of evaporation of new water. He now uses tap water for these applications and generally runs 300-500 gallons through one in the course of a summer. (Sets up in a park and gives rides to kids.) He does an acid scaling of the boilers every few years. Also, a steam iron evaporates a fair amount of water and most people just use tap. Mine is about 10 years old and shows very little scale. We have a steam humidifier in our house that runs most of the winter. Every spring I take it apart and clean the scale out because the owners manual says to. It's less than a teaspoon full.
My conclusion is that in a closed system where there is no evaporative loss, there simply isn't enough mineral content in two or three gallons of water to make any difference. One day when you have nothing better to do, just boil 2 gallons of water until it is completely evaporated and see how much scale you actually have left.
However, the cost is negligible and if it makes you feel better, do it.